In this chapter we study the turnpike property for the nonconvex optimal control problems described by the differential inclusion . We study the infinite horizon problem of maximizing the functional as T grows to infinity. The purpose of this chapter is to avoid the convexity conditions usually assumed in turnpike theory. A turnpike theorem is proved in which the main conditions are imposed on the mapping a and the function u. It is shown that these conditions may hold for mappings a with nonconvex images and for nonconcave functions u.